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# Systems of equations with elimination: King's cupcakes

Sal uses simple elimination to figure out how many cupcakes are eaten by children and adults. Created by Sal Khan.

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• I understand the math and the method. I graphed all of the problems with no trouble and I got the correct answers from the x and y axes. What I don't understand is how this works. It seems almost magical. Two lines intersect and Ka-Boom, you have the two solutions. I feel I am missing something important but I can't see it. That's why It seems magical. •  When you solve a system of equations, the whole purpose is to find how the 2 equations relate to each other, and whether or not they have a common solution. The common solution is the point where the 2 lines intersect because it is a point that sits on both lines.
• I love to drink my cupcakes () • I don't understand why Sal over complicated this. Within the first 5 seconds of seeing " 500a + 200c = 2900" and "500a + 300c = 3100", I knew the answer. I found this by observing the difference between the two equations. Let me explain, in both equations, 500a does not change, it stays the same throughout. which means that the only difference between the two equations is that the amount of C's or children.
Because of that, I was able to tell that 1c =2, because adding 100c, with A (or Adults) remaining static, added 200 to the final product. which mean that c was a variable of 2. Once I knew this, I went back to the first equation(500a + 200c = 2900), plugged in 2 for c, subtracted 400 from 2900, then divided 2500 by 500, which equals 5, the variable of A. So I ask you, is this a special occurrence that just happens to work for a few equations? Or if not, why not just use this uncomplicated way, which you can do in your head? •  Because he is teaching an algebraic method to solve a problem. Different people use different methods to solve equations. This is part of an 8th grade math curriculum enhancement. So while it seems easier to solve in your head, it is only that easy once you have learned how to do it....like he explained here :)
• Just to let you know Sal can draw like crazy. Does he only use the computer? I tried but my work is all sloppy! • Ok, reading through the comments it seems like there a lot of diffewrent ways to solve systems of equation. Can someone give me a quick list? I would like to try other ways to see if I can wrap my head around it easier.

P.S.
I don't mind if there are no videos for it on Khan Academy as long as I am reffered to a explanation. • Sal is definitely human, and not a robot, cause humans make mistakes. children drink two cups...  • Because each adult ate 5 cupcakes,and each child ate 2. There were 500 adults and 200 children. So if each adult ate 5 cupcakes and there were 500 adults,then you would multiply 500 by five. And it's the same with the children. If each child ate 2 cupcakes and there were 200 children,then you would multiply 200 by 2. And then you add the two answers together,and you have 2900.
• is there any other ways to solve this specific equation that is harder or easier in factor? • can you subtract the orange from blue instead ? Why doesn't sal do that • I was trying to solve this problem with the substitution method because I get confused in the elimination one. but I couldn't find the answer, even after many tries. so I just wanted to confirm if we can solve the equation that sal is explaining in this video with substitution method or not. and also wanted to know if there are certain particular was to solve different equations.

sorry for a long query, but would help if solved • It seems slightly more difficult to me in this case, but it can be done. Here are the steps:
500a+200c=2900
500a+300c=3100
First, manipulate one of the equations to isolate one variable:
500a+200c=2900
500a=2900-200c
a=2900/500-(200/500)c
Next, substitute 2900/500-(200/500)c in for a in the other equation:
500(2900/500-(200/500)c)+300c=3100
2900-200c+300c=3100
2900+100c=3100
100c=200
c=2
Now substitute 2 for c in one of the equations to find a:
500a+200(2)=2900
500a+400=2900
500a=2500
a=5
Finally, check this solution in the other equation:
500(5)+300(2)?=3100
2500+600?=3100
3100=3100
So, yes, you can use substitution, but it seems to me that in this case elimination is easier. I think that most systems of equations could be solved in any of the ways that are used to solve systems of equations, but certain ways might be easier in certain cases.